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Chapter 3

Q. 3.22

The industrial process for making the ammonia used in fertilizer, explosives, and many other products is based on the reaction between nitrogen and hydrogen at high temperature and pressure:

N_{2}(g) + 3 H_{2}(g) → 2 NH_{3}(g)

If 18.20 kg of NH_{3} is produced by a reaction mixture that initially contains 6.00 kg of H_{2} and an excess of N_{2}, what is the percent yield of the reaction?

Step-by-Step

Verified Solution

Collect and Organize We know that the actual yield of NH_{3} is 18.20 kg. We also know that the reaction mixture initially contained 6.00 kg of H_{2} and that H_{2} must be the limiting reactant because the problem specifies the presence of excess N_{2}. We need to find the percent yield.

Analyze We need to use the mass of H_{2} to calculate how much NH_{3} could have been produced— the theoretical yield. We can then use the theoretical yield and the actual yield to calculate percent yield. We need the molar masses of H_{2} and NH_{3} and the stoichiometry of the reaction, which tells us that 2 moles of NH_{3} are produced for every 3 moles of H_{2} consumed.

Solve The molar masses we need are:

\mathscr{M}_{H_{2}} = 2(1.008  g/mol) =2.016  g/mol

\mathscr{M}_{NH_{3}} =14.01  g/mol + 3(1.008  g/mol) = 17.03  g/mol

We calculate the theoretical yield of NH_{3}:

6.00  \sout{kg  H_{2}}\times \frac{10^{3}  \sout{g  H_{2}}}{1  \sout{kg  H_{2}}} \times \frac{1  \sout{mol  H_{2}}}{2.016  \sout{g  H_{2}}} \times \frac{2  \sout{mol  NH_{3}}}{3  \sout{mol  H_{2}}} \times \frac{17.03  \sout{g  NH_{3}}}{1  \sout{mol  NH_{3}}} \times \frac{1  kg  NH_{3}}{10^{3}  \sout{g  NH_{3}}} =33.8  kg  NH_{3}

Then we divide the actual yield by this theoretical yield to determine the percent yield:

\frac{18.20  \sout{kg  NH_{3}}}{33.8  \sout{kg  NH_{3}}} \times 100 \%=53.8\%

Think About It A yield of about 54% may seem low, but it may be the best that can be achieved for a particular process. A great deal of chemical research goes into trying to improve the percent yield of industrial chemical reactions.